EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 5 / No 6 (2010) Math. Model. Nat. Phenom., 5 6 (2010) 109-138 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 6, 2010
Ecology (Part 2)
Page(s) 109 - 138
DOI https://doi.org/10.1051/mmnp/20105606
Published online 08 April 2010
  1. L.J.S. Allen, M. LanglaisC.J. Phillips. The dynamics of two viral infections in a single host population with applications to hantavirus. Math. Biosci., 186 (2003), 191–217. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  2. R.M. Anderson, H.C. Jackson, R.M. MayA.D.M. Smith. Population dynamics of fox rabies in Europe. Nature, 289 (1981), 765–771. [CrossRef] [PubMed] [Google Scholar]
  3. V. Andreasen. Multiple times scales in the dynamics of infectious diseases. Mathematical Approaches to Problems in Resource Management and Epidemiology (C. Castillo-Chavez, S.A. Levin, C.A. Shoemaker, eds.), 142–151, Springer, Berlin Heidelberg, 1989. [Google Scholar]
  4. V. Andreasen, J. LinS.A. Levin. The dynamics of cocirculating influenza strains conferring partial cross-immunity. J. Math. Biol., 35 (1997), 825–842. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  5. C. Banerjee, L.J.S. AllenJ. Salazar-Bravo. Models for an arenavirus infection in a rodent population: consequences of horizontal, vertical and sexual transmission. Math. Biosci. Engin., 5 (2008), 617–645. [CrossRef] [Google Scholar]
  6. F.B. Bang. Epidemiological interference. Intern. J. Epidemiology, 4 (1975), 337–342. [CrossRef] [Google Scholar]
  7. C.J. BriggsH.C.J. Godfray. The dynamics of insect-pathogen interactions in stage-structured populations. The American Naturalist, 145 (1995), 855–887. [CrossRef] [Google Scholar]
  8. C. Castillo-Chavez, H.W. Hethcote, V. Andreasen, S.A. LevinW.M. Liu. Epidemiological models with age structure, proportionate mixing, and cross-immunity. J. Math. Biol., 27 (1989), 233–258. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  9. T. Dhirasakdanon, H.R. Thieme. Persistence of vertically transmitted parasite strains which protect against more virulent horizontally transmitted strains. Modeling and Dynamics of Infectious Diseases (Z. Ma, Y. Zhou, J. Wu, eds.), 187–215, World Scientific, Singapore, 2009. [Google Scholar]
  10. O. DiekmannM. Kretzschmar. Patterns in the effects of infectious diseases on population growth. J. Math. Biol., 29 (1991), 539–570. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  11. K. Dietz. Epidemiologic interference of virus populations. J. Math. Biol., 8 (1979), 291–300. [MathSciNet] [PubMed] [Google Scholar]
  12. K. Dietz. Overall population patterns in the transmission cycle of infectious disease agents. Population Biology of Infectious Diseases (R.M. Anderson, R.M. May, eds.), 87–102, Springer, Dahlem Konferenzen, Berlin, 1982. [Google Scholar]
  13. S.H. Faeth, K.P. HadelerH.R. Thieme. An apparent paradox of horizontal and vertical disease transmission. J. Biol. Dyn., 1 (2007), 45–62. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  14. Z. FengH.R. Thieme. Recurrent outbreaks of childhood diseases revisited: the impact of isolation. Math. Biosci., 128 (1995), 93–130. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  15. Z. FengH.R. Thieme. Endemic models with arbitrarily distributed periods of infection. II. Fast disease dynamics and permanent recovery. SIAM J. Appl. Math., 61 (2000), 983–1012. [CrossRef] [MathSciNet] [Google Scholar]
  16. L.Q. Gao, J. Mena-Lorca, H.W. Hethcote. Variations on a theme of SEI endemic models. Differential Equations and Applications to Biology and Industry (M. Martelli, C.L. Cooke, E. Cumberbatch, B. Tang, H.R. Thieme, eds.), 191–207, World Scientific, Singapore, 1996. [Google Scholar]
  17. W.M. GetzJ. Pickering. Epidemic models: thresholds and population regulation. The American Naturalist, 121 (1983), 892–898. [CrossRef] [Google Scholar]
  18. D. Greenhalgh. Some results for an SEIR epidemic model with density dependence in the death rate. IMA J. Math. Appl. Med. Biol., 9 (1992), 67–106. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  19. D. Greenhalgh. Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity. Math. Comput. Modelling, 25 (1997), 85–107. [CrossRef] [MathSciNet] [Google Scholar]
  20. J.V. GreenmanP.J. Hudson. Infected coexistence instability with and without density-dependent regulation. J. Theor. Biol., 185 (1997), 345–356. [CrossRef] [Google Scholar]
  21. E.R. Haine. Symbiont-mediated protection. Proc. R. Soc. B, 275 (2008), 353–361. [CrossRef] [Google Scholar]
  22. H.W. Hethcote, S.A. Levin. Periodicity in epidemiological models. Applied Mathematical Ecology (S.A. Levin, T.G. Hallam, L.J. Gross, eds.), 193–211, Springer, Berlin Heidelberg, 1989. [Google Scholar]
  23. H.W. Hethcote, H.W. StechP. van den Driessche. Nonlinear oscillations in epidemic models. SIAM J. Appl. Math., 40 (1981), 1–9. [CrossRef] [MathSciNet] [Google Scholar]
  24. H.W. Hethcote, W. WangY. Li. Species coexistence and periodicity in host-host-pathogen models. J. Math. Biol., 51 (2005), 629–660. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  25. H.W. HethcoteJ. Pickering. Infectious disease and species coexistence: a model of Lotka-Volterra form. Am. Nat., 126 (1985), 196–211. [CrossRef] [Google Scholar]
  26. M. Iannelli, M. MartchevaX.-Z. Li. Strain replacement in an epidemic model with super-infection and perfect vaccination. Math. Biosci., 195 (2005), 23–46. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. J. Li, Y. Zhou, Z. MaJ.M. Hyman. Epidemiological models for mutating pathogens. SIAM J. Appl. Math., 65 (2004), 1–23. [CrossRef] [MathSciNet] [Google Scholar]
  28. J. Lin, V. AndreasenS.A. Levin. Dynamics of influenza A drift: the linear three-strain model. Math. Biosci., 162 (1999), 33–51. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  29. M. Lipsitch, S. SillerM.A. Nowak. The evolution of virulence in pathogens with vertical and horizontal transmission. Evolution, 50 (1996), 1729–1741. [CrossRef] [PubMed] [Google Scholar]
  30. W.-m. Liu. Dose-dependent latent period and periodicity of infectious diseases. J. Math. Biol., 31 (1993), 487–494. [PubMed] [Google Scholar]
  31. C.M. Lively, K. Clay, M.J. WadeC. Fuqua. Competitive co-existence of vertically and horizontally transmitted diseases. Evolutionary Ecology Res., 7 (2005), 1183–1190. [Google Scholar]
  32. M. Martcheva. On the mechanisms with strain replacement in epidemic models with vaccination. Current Developments in Mathematical Biology (R.C. John Boucher, K. Mahdavi, eds.), 149–165, World Scientific, Hackensack, 2007. [Google Scholar]
  33. M. MartchevaS.S. Pilyugin. The role of coinfection in multidisease dynamics. SIAM J. Appl. Math., 66 (2006), 843–872. [CrossRef] [MathSciNet] [Google Scholar]
  34. G. MeijerA. Leuchtmann. The effects of genetic and environmental factors on disease expression (stroma formation) and plant growth in Brachypodium sylvaticum infected by Epichloë sylvatica. OIKOS, 91 (2000), 446–458. [CrossRef] [Google Scholar]
  35. F.A. MilnerA. Pugliese. Periodic solutions: a robust numerical method for an S-I-R model of epidemics. J. Math. Biol., 39 (1999), 471–492. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  36. M. Nuño, Z. Feng, M. MartchevaC. Castillo-Chavez. Dynamics of two-strain influenza with isolation and partial cross-immunity. SIAM J. Appl. Math., 65 (2005), 964–982. [CrossRef] [MathSciNet] [Google Scholar]
  37. A. Pugliese. An S→E→I epidemic model with varying population size. Differential Equations Models in Biology, Epidemiology and Ecology (S. Busenberg, M. Martelli, eds.), 121–138, Springer, Berlin Heidelberg, 1991. [Google Scholar]
  38. K. Saikkonen, S.H. Faeth, M. HelanderT.J. Sullivan. Fungal endophytes: a continuum of interactions with host plants. Annu. Rev. Ecol. Syst., 29 (1998), 319–343. [CrossRef] [Google Scholar]
  39. J.H. Swart. Hopf bifurcation and stable limit cycle behavior in the spread of infectious disease, with special application to fox rabies. Math. Biosci., 95 (1989), 199–207. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  40. H.R. Thieme. Stability change of the endemic equilibrium in age-structured models for the spread of S-I-R type infectious diseases. Differential Equations Models in Biology, Epidemiology and Ecology (S. Busenberg, M. Martelli, eds.), 139–158, Springer, Berlin Heidelberg, 1991. [Google Scholar]
  41. H.R. Thieme. Mathematics in Population Biology. Princeton University Press, Princeton, 2003. [Google Scholar]
  42. H.R. ThiemeC. Castillo-Chavez. How may infection-age dependent infectivity affect the dynamics of HIV/AIDS?. SIAM J. Appl. Math., 53 (1993), 1447–1479. [CrossRef] [MathSciNet] [Google Scholar]
  43. H.R. Thieme, A. TridaneY. Kuang. An epidemic model with post-contact prophylaxis of distributed length. II. Stability and oscillations if treatment is fully effective. Math. Model. Nat. Phenom., 3 (2008), 267–293. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  44. P. van den DriesscheM.L. Zeeman. Disease induced oscillations between two competing species. SIAM J. Appl. Dyn. Sys., 3 (2004), 601–619. [Google Scholar]
  45. E. Venturino. The effects of diseases on competing species. Math. Biosci., 174 (2001), 111–131. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.